Abstract
The next step in preparing the completeness proof of the Q calculi is to show that any μ-hypercomplete set α is embeddable into a structure 〈W, R, Φ〉 satisfying certain conditions outlined in 10.0 already. As one would guess, we can assume here that 〈W, R〉 is a tree with the top w 0∈ W, where Φ(w 0)= α, our starting set. We shall compress the pair 〈W, R〉 into a partially ordered set Σ⊂ω, where Σ will be called an index tree (Section 13.1). Then we introduce the notion of μtree structures 〈Σ, Φ〉 where Φ is a function defined on Σ, and the values of Φ are μ-hypercomplete sets (Section 13.2). Finally, we show (in Section 13.3) the embeddability of α into a so-called complete μ-tree structure. (The omitted relation R can be defined by means of the partial ordering on Σ; but we shall need R only in the next §.)
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Ruzsa, I. (2001). Tree Structures. In: Modal Logic with Descriptions. Nijhoff International Philosophy Series, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2294-0_14
Download citation
DOI: https://doi.org/10.1007/978-94-017-2294-0_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8266-4
Online ISBN: 978-94-017-2294-0
eBook Packages: Springer Book Archive